The coronavirus pandemic has created a new awareness of epidemics, and insurance companies have been reminded to consider the risk related to infectious diseases. This paper extends the traditional multi-state models to include epidemic effects. The main idea is to specify the transition intensities in a Markov model such that the impact of contagion is explicitly present in the same way as in epidemiological models. Since we can study the Markov model with contagious effects at an individual level, we consider individual risk and reserves relating to insurance products, conforming with the standard multi-state approach in life insurance mathematics. We compare our notions with other but related notions in the literature and perform numerical illustrations.

This paper surveys some statistical models of survival data. A basic model of a random lifetime is defined, and censoring is introduced. Methods based on observations of small segments of lifetimes are compared. Markov and semi-Markov (multiple state) models are recommended as well-understood and flexible models well suited to actuarial data. A Poisson model is discussed as an approximation to a two state model, while traditional Binomial-type models are shown to be more restricted and less tractable than multiple state models.

Alzheimer's disease (AD) accounts for a significant proportion of long-term care costs. The recent discovery that the ε4 allele of the ApoE gene indicates a predisposition to earlier onset of AD raises questions about the potential for adverse selection in long-term care insurance, about long-term care costs in general, and about the potential effects on costs of gene therapy, or better targetted treatments for AD. This paper describes a simple Markov model for AD, and the estimation of the transition intensities from the medical and epidemiological literature.

We consider Markov models for growth of populations subject to catastrophes. Emphasis is placed on discrete-state models where immigration is possible and the catastrophe rate is population-dependent. Explicit formulas for descriptive quantities of interest are derived when catastrophes reduce population size by a random amount which is either geometrically, binomially or uniformly distributed. Comparison is made with continuous-state Markov models in the literature in which population size evolves continuously and deterministically upwards between random jumps downward.